A novel multi-objective salp swarm algorithm (MSSA)-based cascade PD–(1 + PI) controller is proposed for a magnetorheological (MR)-damped vehicle suspension system. The control framework comprises two nested controllers: a system controller based on a cascade PD–(1 + PI) structure tuned via MSSA, and a damper controller utilizing the standard signum function method (SFM). Comprehensive simulations are conducted in MATLAB/Simulink using a five-degree-of-freedom (5-DOF) half-vehicle model incorporating a modified Bouc–Wen formulation. System performance is evaluated under double-bump excitation, random-road excitation, and braking maneuvers based on the New European Driving Cycle (NEDC) to investigate both steady-state and transient bounce–pitch dynamics, as well as the coupling between ride comfort and braking behavior. The longitudinal acceleration derived from the NEDC profile is incorporated into the pitch dynamics to account for braking-induced load transfer effects. Key performance criteria, including suspension deflection, tire deflection, body vertical acceleration, and pitch response, are analyzed in both the time and frequency domains. Comparative results demonstrate that the proposed MSSA-tuned PD–(1 + PI) controller outperforms conventional passive suspension, MR-passive (zero-voltage applied), MSSA-tuned PID, MSSA-tuned FOPID, and MSSA-tuned fuzzy PID controllers. The proposed approach significantly enhances ride comfort and vehicle stability, achieving reductions of up to 57% in suspension deflection, 32% in tire deflection, and 41% in driver body acceleration.
El-Taweel et al. (Thu,) studied this question.